Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D47 |
| commutator | C23×C47 | C24 |
| Frattini | C23 | C23×D47 |
| Fitting | C2×#95×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C2×#95 | D47 |
| hypocenter | C47 | C2×#394 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic47⋊C4 | C2 | semidirect |
| 3. C22×(C2×D47)⋊C4 | C2 | semidirect |
| 4. C22×(C2×D47)⋊C4 | C2 | semidirect |
| 5. #15689041 | C2 | direct (N × H) |
| 6. C2×#95×C47 | C2 | semidirect |
| 14. C2×Dic47⋊C4 | C22 | semidirect |
| 17. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 18. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 21. #95×C47 | C22 | semidirect |
| 42. C22×Dic47 | D4 | semidirect |
| 84. C2×Dic47 | C2×D4 | semidirect |
| 109. C2×C47 | #394 | semidirect |
| 121. C2×#95 | D47 | semidirect |
| 122. C47 | C2×#394 | semidirect |
| 137. #95 | C2×D47 | semidirect |
| 225. C2 | #15689041 | direct (N × H) |